Spacetimes as topological spaces, and the need to take methods of general topology more seriously

Abstract

Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology sufficient for the description of spacetime singularities or a topology which incorporates the causal structure? Or both? Is it more preferable to have a topology with as many physical properties as possible, whose description might be complicated and counterintuitive, or a topology which can be described via a countable basis but misses some important information? These are just a few from the questions that we ask in this Chapter, which serves as a critical review of the terrain and contains a survey with remarks, corrections and open questions.

Invited book Chapter, to appear in book: Current Trends in Mathematical Analysis and Its Interdisciplinary ApplicationsEdition: Birkhauser, imprint of Springer

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• Dear Qubitzers, GR=QM
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• The causal order on the ambient boundary
• On Two Topologies that were suggested by Zeeman
• The Order on the Light Cone and its induced Topology
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• On the Possibility of Singularities on the Ambient Boundary
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Cited by in corpus (2)

• Natural vs. Artificial Topologies on a Relativistic Spacetime
• On the Causal and Topological Structure of the $2$-Dimensional Minkowski Space